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A research Van de Graaff generator has a 2.00-m- diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generator. What is its energy in MeV at this distance?

(a) $V=45.0 \times 10^{6} \mathrm{V}$(b) $r^{\prime}=45.0 \mathrm{m}$(c) $U_{e}=132 \mathrm{MeV}$

Physics 102 Electricity and Magnetism

Chapter 19

Electric Potential and Electric Field

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Hope College

University of Sheffield

McMaster University

Lectures

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All right, swing this problem. We're considering the vinegar of generator. Basically, it is just the sphere. Ah, was Reedus. Let's see, The radius is two meters and that the charges on the surface of this generator is five meeting columns. You call this one in? Ah, in part A. We want to find out to the potential at the surface of this sphere. So you equal one over. So this is You are so this scepter are which is the radius of the sphere you call one over four pi. Absolute knots and times Q over our Okay. Accuse right here. And ours The radius. And you can see that it's very kuo. 45 mega votes and in part B so Ah, let's see. So suppose we have a location right here and we know the potential at this point is one making one. Make it you make a volts. So want to find other distance from this point to the scent of the spear? So again, we just say that to you. Ah, Smarr equal one over for pie. Absolutely not times Q over smart and this equal one mega volts. So Q is against equal five minute columns. And the only unknown variable is this distance so confined out are equal 45 meters. Okay. And in Parsi, uh, to suppose we have our extradition with three electrons missing again, this is this fear. This is a generator. And we release this oxygen Adam from the surface of the sphere to this location. Ah, where the location is the one that we found in the party. So the oxygen travels from the cities or the sphere to this location. And, uh, we want to find the energy off this. Ah, oxygen atom. So because we know the potential and the surface of the sphere, we are equal 45 mega votes, right? So this is from that. That is what we found in part a into the potential at this point. V. Smarr equal one mega volts. This is a waterway founding part being. So the potential difference between these two points v equal v r minus B R, which is 44 mega votes. Right? So the total energy that the oxygen Adam had a can of attention is, uh, equal. Delta v. Times two. We're I don't see this. This capital Q is the charge the charge of the extra one on accident. Adam, which equal three. Hey, so it equals R V times free. And this gives you the energy of this, uh, extra Adam when it reaches that. Ah, this location and this better is 1 32 mega electro volts.

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